The poll provides a view of the impact of bin Laden’s death in a state widely viewed as a bellwether for Obama’s chances for reelection nationally. The interviews were already underway when Obama delivered the news late in the evening of May 1; 677 were conducted before the announcement, with 503 afterward.

Against all five potential GOP contenders tested in the poll, Obama stretched his margins after the death of bin Laden. In a hypothetical matchup against former Massachusetts governor Mitt Romney, for example, interviews before the bin Laden announcement showed voters splitting 48 percent for the president and 46 percent for Romney. Afterward, Obama edged ahead, 51 to 44 percent.

Still, big vulnerabilities remain for the president, the first Democratic presidential nominee to win Virginia in more than 40 years. More than half of all Virginia voters are dissatisfied, even angry, with the Obama administration’s policies, and a vast majority retains a bleak view of the economy. Those opinions did not change with bin Laden’s death, leaving open the question of whether, or how long, the spike in Obama’s fortunes will last.

The poll reveals the movability of voters in Virginia, which firmly established itself as a new battleground in 2008. Two years later, in the tea-party-infused, low-turnout elections of 2010, Virginia swung in the opposite direction, ousting three of the state’s six Democratic congressmen.

The question heading into next year’s presidential election is whether the electorate will look more like the one that voted for Obama in 2008 or the one that showed up in 2010. The Post poll shows that the coalition of voters who turned out for Obama in 2008 is willing, at least in the wake of the bin Laden announcement, to consider doing so again.

“It reaffirmed my decision to vote for him in the first place,” said Kim Bentley, 29, a technology worker from Virginia Beach who is registered as an independent and leans Republican.

Even people who voted against Obama — and are likely to do so again — said they view him in a more favorable light now.

“Ever since Osama got killed, his speeches have been very authoritative,” said Michael Moran, 25, a truck driver from Virginia Beach who typically votes Republican. “I’ve seen a lot more power coming from the office in the last few days. . . . Like or hate his policies, you have to respect him. He’s in­cred­ibly intelligent and a strong leader and at times can bring the country together.”

Obama built a coalition of young, urban-dwelling and minority voters that propelled him to victory in 2008, and few places exemplify that better than Virginia. A complex, growing state with a large African American population and an exploding Latino presence, Virginia combines the conservatism and economic pessimism of rural America with the independent-mindedness of swing voters of military-heavy exurbs and the more progressive priorities of the affluent and highly educated Washington suburbs.

A large contingent of the Obama coalition stayed home in 2010. Obama’s major challenge next year is bringing it out again — and holding it together.

At this stage, with his bin Laden bump included, the president maintains much of the support he had 31/2 years ago. Fully two-thirds of voters younger than 30 approve of the job Obama is doing; in 2008, he won 60 percent of the state’s young voters. He’s at a significantly lower 46 percent approval among seniors, but that’s the same percentage he won against the 2008 Republican nominee, Sen. John McCain (Ariz.), according to exit polls.

Similarly, Obama’s approval rating among African American voters matches the 92 percent he won in 2008; his 38 percent approval among whites does so almost exactly — he scored 39 percent of white voters.

Virginia also features the booming exurbs that were once the exclusive province of Republicans but where Democrats, including Obama and former Virginia governor Timothy M. Kaine — who is running for the U.S. Senate next year — made many of their gains over the past decade.

Obama’s — and Kaine’s — chances in a state such as Virginia could turn on their fortunes in those exurbs, many of them just outside the Capital Beltway. Yet the challenge remains high — exurban Virginia voters turned away from Democrats in 2009 and 2010.

Obama won 51 percent of the exurban vote in 2008 but captures a 45 percent exurban approval rating in the Post poll, a figure that includes interviews conducted before and after the news of bin Laden’s death.

Overall, 52 percent of all Virginians say they approve of the way Obama is handling his job as president, putting him near his 2008 vote tally in the state. That year, Obama defeated McCain 53 percent to 46 percent to become the first Democrat to win the state since Lyndon Johnson in 1964.

Obama’s approval rating combines more middling ratings before bin Laden’s killing with rosier assessments afterward. In interviews conducted before the news of bin Laden’s death May 1, Obama’s approval was 49 percent, with 46 percent of Virginians expressing disapproval. But in the subsequent three nights, the president’s job approval number leapt to 57 percent, an eight-point bump. Disapproval dropped to 40 percent.

The poll revealed no broad-based reassessment of Obama’s policies.

About half of all Virginians are “dissatisfied” or “angry” about the policies of the Obama administration, with no movement after bin Laden’s death. Nor was there any real change after the announcement in assessments of the major health-care law signed by the president last year.

By some measures, the Virginia electorate is less friendly terrain for Obama than it was in the summer of 2007, when the Democrats were gearing for a big win there. About 56 percent of Virginians say the federal government is trying to do too much that should be left to businesses and individuals; that’s up from 50 percent in June 2007.

Along the same lines, more than half of all Virginians consider themselves to be “fiscal conservatives.” The economy is also seen as being in far worse shape. Nearly nine in 10 see the national economy as in “not so good” or “poor” shape, with the proportion saying poor more than doubling since 2007. Now, nearly three in 10 see themselves as “falling behind financially.”

The poll was conducted April 28 to May 4. Interviews were conducted on conventional and cellular telephones. The results from the full poll of 1,180 adults have a margin of sampling error of plus or minus 3.5 percentage points.

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